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Development of linear and non-linear properties of heart rate control during quiet and active sleep in healthy infants
Journal of Electrocardiology Vol. 28 No. 4 1995
Development of linear and non-linear properties of heart rate control during quiet and active sleep in healthy infants Andreas Patzak Institute o f Physiology Humboldt-Umversity o f Berlin, University Hospital Charit6, Hessische Str. 3-4, 10115 Berlin
Abstract
In this study it is analyzed by linear and non-linear methods, how the control of instantaneous heart rate ( I H ) develops in infants in quiet and active sleep. Ten healthy and term newborns were studied during their first half year of life. Low (LF) and high frequency power (HF) of the spectrum, and the largest Lyapunov exponent (LLE) were calculated from IHR. By means of the surrogatedata-test, significance of LLE with respect to linear correlated ganssian noise was verified. Significant differences were determined between the original and the surrogate data sets (p< 0.001) assuming non-linear properties. LF, I-IF, LLE have irregular developmental patterns during the first month, whereby LLE has a distinct low value on the 21st day. I-IF siguificantly increases between the second and sixth month in quiet sleep, whereas for LF and LLE no significant correlations were found, neither for quiet nor active sleep. Using linear and non-linear methods, the study shows that the system controlling heart rate pass through mainly two different developmental periods: a period of adaptation in the first four weeks, where parameters distinctly vary, followed by a period with clear developmental courses, lasting till the sixth month.
Keywords: heart rate variability - power spectral analysis non-linear analysis - development Introduction
Parameters of heart rate variability (HRV), analyzed in the time and frequency domain by linear methods have been shown as a marker of disturbed vegetative control and heart failure for many years [1, 2]. Recently, "chaotic" properties of IHR were detected by different methods of non-linear dynamics [3]. One of the algorithms used for non-linear analysis is the calculation of the largest Lyapunov exponent which measures the sensitivity of a system to initial conditions, an essential feature of chaotic reacting systems [4]. Until now, it is unclear whether chaotic behavior is more associated with healthy or with disturbed heart control. Moreover, little knowledge exists about the postnatal development of non-linear properties o f IHR. Answering these questions could be helpful for understanding clinical problems such as sudden infant death. Methods
Ten healthy and term newborns (gestationai age: 38-40 weeks, birth weight: 2830-3880 g, umbilical cord-pH: 7.197.36) were studied. 15 polygraphic measurements of about one hour were performed during the first half year of their 356
life. Informed parental consent and local ethics committee approval were obtained. Measurements were performed at the same time of day with a room temperature between 23 and 25 °C and a low noise level. States of wakefulness, active and quiet sleep were determined, paying special attention to motoric behavior, including eye movement and respiration following the criteria of Prechtl [5]. The R waves of a bipolar limb lead of the ECG were detected by hardware and R-R intervals were calculated by a micro computer. Periods of R-R intervals with a length of 70 -130 seconds separated into quiet and active states of sleep were first corrected in case of too short or too long intervals [61. IHR series were interpolated with cubic spliue functions and were resampled to obtain an equidistant time series. Power spectral analysis was performed by means of fast Fourier transform (FFT) and power in the range from 0.02 to 0.2 Hz (low frequency power, LF) and power greater than 0.2 up to 1.5 Hz (high frequency power, HF) was used. The largest Lyapunov exponent was calculated from each time series using the Wolf algorithm [4]. In order to verify the calculation of LLE, surrogate data were created [7], which had the same linear properties as the original data set. This was accomplished by shuffling the phases in the frequency domain. After re-transforming, the largest Lyapunov exponents were calculated from these surrogate data as well. The significance of the differences between the mean values regarding postnatal days and the states of sleep were tested by Students t-Test. The confidence level alpha was set to 0.05. Results
LLE of original and surrogate data differ significandy (p<0.001), indicating non-linear properties. In most of the cases, LLE of original data was slightly positive. LF, I-IF and LLE have developmental patterns in quiet and active sleep which are characterized by irregular courses during the first month. Values are higher immediately after birth and lower at the end of the first month (Fig 1, 2, 3). Except for the low value of LLE on the 21st day, the slopes are not significant. After the first month up to the sixth month HF increases, especially in quiet sleep (slope: 0.14:L-0.07, p<0.05, Fig 1). LF also shows an increasing trend during the same period in quiet sleep, but not for active sleep states (Fig 2). LLE does not show any significant trend neither for quiet not for active sleep after the first month (Fig 3). Transitions between quiet and active sleep are accompanied by distinct changes in rhythmicity. In the first month, LF is significantly higher during active sleep (p<0.05), whereas I-IF and LLE do not systematically change. From the second
Selected Short Papers From the XXllnd International Congress on Electrocardiology
to the sixth month, the differences between the states for LF become smaller and for HF greater. LLE shows no correlation to the sleep states during this time. Jower (a.u.) 30
20 ¸
10"
30
60
90
120
150
180
age (days)
Figure 1 Developmental course of the high frequency component (HF) of the power speOxtLmof IHR series during the first half year of life for quiet (solid line) and active sleep (broken line, mean-~S.E.M., n = 10). 3ower (a.u.)
81)
. . . .
,L
surrogate data differ significantly in this study. This indicates non-linear properties in IHR control. The slighty positive LLE values hint at a sensitivity of IHR series to initial conditions. This is in agreement with other studies where comparable measures of complexity were used in infants [8]. In contrast to the spectral parameters of IHR, the LLE does not show a clear trend during postnatal development. Moreover, no significant differences in LLE exist between states of sleep. We speculate that non-linear properties measured by LLE are well developed at birth and that these properties are independent of states of activity in sleep. All parameters show more irregular courses during the first month in comparison with the period between the second and the sixth month. Different individual developmental courses as well as immature IHR control may be the reasons. After this period of adaptation, LLE and the rhythmic parameters have more stable courses. LF and HF develop into patterns similar to those in sleeping adults, expressing the maturation of vegetatively controlled sleep organization. This study shows that by linear and non-linear analysis one can reveal the complexity of the I H control and its maturation in steps of adaptation and of stabilization during the first half year of life in humans.
Acknowledgement The author thanks Mrs. Uta Stangenberg and Dipl.-Ing. Dirk Lewinsohn for their assistance during measurements and data analysis. The study was supported by the Bundesministerium fitr Forsehung und Technik, Grant No. FK 01ZZ9101.
................................................................
21) 0
I
I
I
I
I
I
30
60
90
120
150
180
age (days)
Figure 2 Developmental course of the low frequency component (LF) of the power spectrum of IHR series during the first half year of life for quiet (solid line) and active sleep (broken line, meaniS.E.M., n=10).
[1]
[2]
larl~est Lyapunov,-exponent 0.10 -
0 . 0 5 "J
rJ i ...............................
, ..........................
[3] 0
[4] -0.05-
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30
60
90
120
150
180
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[5]
age (days)
Figure 3 Developmental course of the largest Lyapunov exponent (LLE) of IHR series during the first half year of life for quiet (solid line) and active sleep (broken line, mean_4:S.E.M., n=10).
Discussion When applying methods of non-linear dynamics on biological times series, some problems arise due to the instationarity of time series and varying noise level. In order to check the calculation of LLE, the surrogate data method was used [7]. It could be shown that LLE from original and
[6] [7]
[8]
References J.P. Saul, Y. Arai, R.D. Berger, L.S. Lilly, W.S. Colucci, and R.J. Cohen. Assessment of autonomic regulation in chronic congestive heart failure by heart rate spectral analysis. Am J Cardiol 61, pp. 1292-1299, 1988 M Lislmer, S. Akselrod, V. Mot Avi, O. Oz, M. Divon, and M. Ravid. Spectral analysis of heart rate fluctuations. A non-invasive, sensitive method for early diagnosis of autonomic neuropathy in diabetes mellitus. JAutonom NervSystem 19, pp.119-125, 1987 A. Babloyantz, A. Destexhe. Is the normal heart a periodic oscillator? Bioi Cybern 58, pp. 203-211, 1988 A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano. Determining Lyapunov exponents from a time series. Physica 16, pp. 285-317, 1985 H.F.R. Prechtl. The behavioral states of the newborn infant (a review). Brain Res 76, pp. 185-212, 1974 W. Orlow, A. Patzak. Analysis of disturbed ECGs in newborns. (Abstract)J Electrocardiol. 26(Suppl.), p. 37, 1993 J. Theiler, B. Galdrikian, A. Longtin, S. Eubank, JD. Farmer. Using surrogate data to detect non-linearity in time series. In: Non-linear Modelling and Forecasting. vol. XII of SFI Studies in the Sciences of Complexity (Casdagli M, Eubank S, eds.), pp. 163-188, AddisonWesley, 1992 S.M. Pincns, T.I~ Cummings, G.G. Haddad. Heart rate control in normal and aborted-SIDS infants. Am J Physio1264, pp. R638-646, 1993
Development of linear and non-linear properties of heart rate control during quiet and active sleep in healthy infants Andreas Patzak Institute o f Physiology Humboldt-Umversity o f Berlin, University Hospital Charit6, Hessische Str. 3-4, 10115 Berlin
Abstract
In this study it is analyzed by linear and non-linear methods, how the control of instantaneous heart rate ( I H ) develops in infants in quiet and active sleep. Ten healthy and term newborns were studied during their first half year of life. Low (LF) and high frequency power (HF) of the spectrum, and the largest Lyapunov exponent (LLE) were calculated from IHR. By means of the surrogatedata-test, significance of LLE with respect to linear correlated ganssian noise was verified. Significant differences were determined between the original and the surrogate data sets (p< 0.001) assuming non-linear properties. LF, I-IF, LLE have irregular developmental patterns during the first month, whereby LLE has a distinct low value on the 21st day. I-IF siguificantly increases between the second and sixth month in quiet sleep, whereas for LF and LLE no significant correlations were found, neither for quiet nor active sleep. Using linear and non-linear methods, the study shows that the system controlling heart rate pass through mainly two different developmental periods: a period of adaptation in the first four weeks, where parameters distinctly vary, followed by a period with clear developmental courses, lasting till the sixth month.
Keywords: heart rate variability - power spectral analysis non-linear analysis - development Introduction
Parameters of heart rate variability (HRV), analyzed in the time and frequency domain by linear methods have been shown as a marker of disturbed vegetative control and heart failure for many years [1, 2]. Recently, "chaotic" properties of IHR were detected by different methods of non-linear dynamics [3]. One of the algorithms used for non-linear analysis is the calculation of the largest Lyapunov exponent which measures the sensitivity of a system to initial conditions, an essential feature of chaotic reacting systems [4]. Until now, it is unclear whether chaotic behavior is more associated with healthy or with disturbed heart control. Moreover, little knowledge exists about the postnatal development of non-linear properties o f IHR. Answering these questions could be helpful for understanding clinical problems such as sudden infant death. Methods
Ten healthy and term newborns (gestationai age: 38-40 weeks, birth weight: 2830-3880 g, umbilical cord-pH: 7.197.36) were studied. 15 polygraphic measurements of about one hour were performed during the first half year of their 356
life. Informed parental consent and local ethics committee approval were obtained. Measurements were performed at the same time of day with a room temperature between 23 and 25 °C and a low noise level. States of wakefulness, active and quiet sleep were determined, paying special attention to motoric behavior, including eye movement and respiration following the criteria of Prechtl [5]. The R waves of a bipolar limb lead of the ECG were detected by hardware and R-R intervals were calculated by a micro computer. Periods of R-R intervals with a length of 70 -130 seconds separated into quiet and active states of sleep were first corrected in case of too short or too long intervals [61. IHR series were interpolated with cubic spliue functions and were resampled to obtain an equidistant time series. Power spectral analysis was performed by means of fast Fourier transform (FFT) and power in the range from 0.02 to 0.2 Hz (low frequency power, LF) and power greater than 0.2 up to 1.5 Hz (high frequency power, HF) was used. The largest Lyapunov exponent was calculated from each time series using the Wolf algorithm [4]. In order to verify the calculation of LLE, surrogate data were created [7], which had the same linear properties as the original data set. This was accomplished by shuffling the phases in the frequency domain. After re-transforming, the largest Lyapunov exponents were calculated from these surrogate data as well. The significance of the differences between the mean values regarding postnatal days and the states of sleep were tested by Students t-Test. The confidence level alpha was set to 0.05. Results
LLE of original and surrogate data differ significandy (p<0.001), indicating non-linear properties. In most of the cases, LLE of original data was slightly positive. LF, I-IF and LLE have developmental patterns in quiet and active sleep which are characterized by irregular courses during the first month. Values are higher immediately after birth and lower at the end of the first month (Fig 1, 2, 3). Except for the low value of LLE on the 21st day, the slopes are not significant. After the first month up to the sixth month HF increases, especially in quiet sleep (slope: 0.14:L-0.07, p<0.05, Fig 1). LF also shows an increasing trend during the same period in quiet sleep, but not for active sleep states (Fig 2). LLE does not show any significant trend neither for quiet not for active sleep after the first month (Fig 3). Transitions between quiet and active sleep are accompanied by distinct changes in rhythmicity. In the first month, LF is significantly higher during active sleep (p<0.05), whereas I-IF and LLE do not systematically change. From the second
Selected Short Papers From the XXllnd International Congress on Electrocardiology
to the sixth month, the differences between the states for LF become smaller and for HF greater. LLE shows no correlation to the sleep states during this time. Jower (a.u.) 30
20 ¸
10"
30
60
90
120
150
180
age (days)
Figure 1 Developmental course of the high frequency component (HF) of the power speOxtLmof IHR series during the first half year of life for quiet (solid line) and active sleep (broken line, mean-~S.E.M., n = 10). 3ower (a.u.)
81)
. . . .
,L
surrogate data differ significantly in this study. This indicates non-linear properties in IHR control. The slighty positive LLE values hint at a sensitivity of IHR series to initial conditions. This is in agreement with other studies where comparable measures of complexity were used in infants [8]. In contrast to the spectral parameters of IHR, the LLE does not show a clear trend during postnatal development. Moreover, no significant differences in LLE exist between states of sleep. We speculate that non-linear properties measured by LLE are well developed at birth and that these properties are independent of states of activity in sleep. All parameters show more irregular courses during the first month in comparison with the period between the second and the sixth month. Different individual developmental courses as well as immature IHR control may be the reasons. After this period of adaptation, LLE and the rhythmic parameters have more stable courses. LF and HF develop into patterns similar to those in sleeping adults, expressing the maturation of vegetatively controlled sleep organization. This study shows that by linear and non-linear analysis one can reveal the complexity of the I H control and its maturation in steps of adaptation and of stabilization during the first half year of life in humans.
Acknowledgement The author thanks Mrs. Uta Stangenberg and Dipl.-Ing. Dirk Lewinsohn for their assistance during measurements and data analysis. The study was supported by the Bundesministerium fitr Forsehung und Technik, Grant No. FK 01ZZ9101.
................................................................
21) 0
I
I
I
I
I
I
30
60
90
120
150
180
age (days)
Figure 2 Developmental course of the low frequency component (LF) of the power spectrum of IHR series during the first half year of life for quiet (solid line) and active sleep (broken line, meaniS.E.M., n=10).
[1]
[2]
larl~est Lyapunov,-exponent 0.10 -
0 . 0 5 "J
rJ i ...............................
, ..........................
[3] 0
[4] -0.05-
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30
60
90
120
150
180
.
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[5]
age (days)
Figure 3 Developmental course of the largest Lyapunov exponent (LLE) of IHR series during the first half year of life for quiet (solid line) and active sleep (broken line, mean_4:S.E.M., n=10).
Discussion When applying methods of non-linear dynamics on biological times series, some problems arise due to the instationarity of time series and varying noise level. In order to check the calculation of LLE, the surrogate data method was used [7]. It could be shown that LLE from original and
[6] [7]
[8]
References J.P. Saul, Y. Arai, R.D. Berger, L.S. Lilly, W.S. Colucci, and R.J. Cohen. Assessment of autonomic regulation in chronic congestive heart failure by heart rate spectral analysis. Am J Cardiol 61, pp. 1292-1299, 1988 M Lislmer, S. Akselrod, V. Mot Avi, O. Oz, M. Divon, and M. Ravid. Spectral analysis of heart rate fluctuations. A non-invasive, sensitive method for early diagnosis of autonomic neuropathy in diabetes mellitus. JAutonom NervSystem 19, pp.119-125, 1987 A. Babloyantz, A. Destexhe. Is the normal heart a periodic oscillator? Bioi Cybern 58, pp. 203-211, 1988 A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano. Determining Lyapunov exponents from a time series. Physica 16, pp. 285-317, 1985 H.F.R. Prechtl. The behavioral states of the newborn infant (a review). Brain Res 76, pp. 185-212, 1974 W. Orlow, A. Patzak. Analysis of disturbed ECGs in newborns. (Abstract)J Electrocardiol. 26(Suppl.), p. 37, 1993 J. Theiler, B. Galdrikian, A. Longtin, S. Eubank, JD. Farmer. Using surrogate data to detect non-linearity in time series. In: Non-linear Modelling and Forecasting. vol. XII of SFI Studies in the Sciences of Complexity (Casdagli M, Eubank S, eds.), pp. 163-188, AddisonWesley, 1992 S.M. Pincns, T.I~ Cummings, G.G. Haddad. Heart rate control in normal and aborted-SIDS infants. Am J Physio1264, pp. R638-646, 1993